9. $$ \sqrt{45}-\sqrt{20}+4 \sqrt{5} \quad 10.2 \sqrt{12}-\sqrt{40}+3 \sqrt{27} $$

Question

UpStudy AI · Accepted Answer

We are given two expressions to simplify:

1) √45 − √20 + 4√5

2) 2√12 − √40 + 3√27

Let’s simplify each step‐by‐step.

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Expression 1: √45 − √20 + 4√5

Step 1. Simplify √45:
  √45 = √(9×5) = √9 × √5 = 3√5.

Step 2. Simplify √20:
  √20 = √(4×5) = √4 × √5 = 2√5.

Step 3. Substitute back into the expression:
  3√5 − 2√5 + 4√5.

Step 4. Combine like terms:
  (3 − 2 + 4)√5 = 5√5.

So the simplified form is 5√5.

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Expression 2: 2√12 − √40 + 3√27

Step 1. Simplify √12:
  √12 = √(4×3) = √4 × √3 = 2√3.
  Then, 2√12 = 2 × 2√3 = 4√3.

Step 2. Simplify √40:
  √40 = √(4×10) = √4 × √10 = 2√10.

Step 3. Simplify √27:
  √27 = √(9×3) = √9 × √3 = 3√3.
  Then, 3√27 = 3 × 3√3 = 9√3.

Step 4. Substitute back into the expression:
  4√3 − 2√10 + 9√3.

Step 5. Combine like terms (the √3 terms):
  (4√3 + 9√3) − 2√10 = 13√3 − 2√10.

So the simplified form is 13√3 − 2√10.

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Final Answers:

1) √45 − √20 + 4√5 = 5√5

2) 2√12 − √40 + 3√27 = 13√3 − 2√10
Simplified answers: 1) √45 − √20 + 4√5 = 5√5 2) 2√12 − √40 + 3√27 = 13√3 − 2√10

9. \( \sqrt{45}-\sqrt{20}+4 \sqrt{5} \quad 10.2 \sqrt{12}-\sqrt{40}+3 \sqrt{27} \)